Response to “Comment on ‘Geometric phase of the gyromotion for charged particles in a time-dependent magnetic field’” Phys. Plasmas 19, 094701 (2012)

The reformulation of our analysis on the geometric phase of the gyromotion J. Liu and H. Qin, Phys. Plasmas 18, 072505 (2011) in terms of spatial angles presented in the comment by Brizard and Guillebon is interesting and correct. The subtlety of whether the adiabatic term associated with the long term average of the variation of pitch angle completely disappears after the gyrophase average is related to where valid approximations are applied. But it has no impact on the main conclusions.